ORIGINAL ARTICLES

Acta Mathematica Sinica

, Volume 16, Issue 1, pp 103-112

First online:

The Existence of BIB Designs

  • Yanxun ChangAffiliated withInstitute of Mathematics, Northern Jiaotong University Email author 

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Abstract

Given any positive integers k≥ 3 and λ, let c(k, λ) denote the smallest integer such that vB(k, λ) for every integer vc(k, λ) that satisfies the congruences λv(v− 1) ≡ 0(mod k(k− 1)) and λ(v− 1) ≡ 0(mod k− 1). In this article we make an improvement on the bound of c(k, λ) provided by Chang in [4] and prove that \( c{\left( {k,\lambda } \right)} \leqslant \exp {\left\{ {k^{{3k^{6} }} } \right\}} \). In particular, \( c{\left( {k,1} \right)} \leqslant \exp {\left\{ {k^{{k^{2} }} } \right\}} \).

Keywords

Wilson’s theorem Balanced incomplete block design PBD-closed

1991 MR Subject Classification

05B